What reparative therapy offers is an origin story, an etiological myth, to explain the genesis of homosexuality. The client accepts and internalizes this story and then resolves it: he moves through a series of interior confrontations with the father wound and the spectre of the overattached mother, he defeats these internal demons, and in doing so, he is healed.
This is a classic form of healing, found in all societies. A Magus figure, a shaman, guru, or psychologist (I think it's Peter Kreeft who points out that the latter are the Priest-class of scientific modernism) claims authority over the cause of illness. This illness may be psychological, physical or spiritual. The Magus tells a story which harkens back to The Beginning, and then symbolically moves the one in need of healing back into that time when the illness first came to be. There is then a confrontation, an interior struggle in which both the medicine man and the patient participate together by invoking the deity who has the power to overcome the ancient evil which is gnawing away at the patient's body or psyche. Through this confrontation, which may take the form of a rigorous psychological trial, the evil is defeated. Both the Magus and the patient return from the past-time and the patient is healed.
Now I personally like my etiological myths to be mythology flavoured: I prefer stories that go back to when the ancestors were wandering in the dream-time, or when the people used to be bears, or when Adam and Eve lived in a perfect garden from the centre of which flowed four rivers. Scientific materialism requires etiological myths that are somewhat less spectacular, that have the illusion of being “objective” and “verifiable.” Hence the reliance of traditional psychoanalysis on “family of origin” narratives to explain all sorts of psychological problems. The original family serves, in these stories, as The Beginning, the psychological beginning of the person's life, and the healing takes place by returning to that time and resolving conflicts there (religious anthropologist Mercea Eliade uses the lovely Latin phrase “in illo tempore” to refer to that special time in which etiological myths take place.)
Putting my personal tastes aside, however, the reparative therapy narrative does offer most of the essential features of a good medicine song. It goes back to The Beginning. In The Beginning, there are evils to be confronted. These evils are archetypally valid, and they exist in a valid archetypal relationship with the Magus figure who is leading the patient back into the past in order to bring him healing. The parasitic, overcontrolling mother is a classic figure in the “father quest,” that is in stories of self-discovery and identity creation. The distant father is an ambiguous figure, he could be a true Father, a Magus figure who the child rejects because he is too forbidding and austere, or he could be a disgraceful father who fails his children because he is too absorbed in himself. In any case, the child confronts these figures, throwing off the yoke of the overcontrolling mother and reconciling with the distant father. The reparative therapists themselves say that their methods are more effective than mere psychotherapy because they use Christian spirituality to bring about reconciliation. This is the invocation of the deity, another important element of true healing stories.
What this means, is that reparative therapy may be effective for some people, but its efficacy relies on the client's ability to buy into the narrative and accept the authority of the therapist. This is where the comment about family of origin stories being “boring and reductive” becomes an issue. If the story that the medicine man tells seems ridiculous, insufficient, or otherwise not compelling to the patient, then the medicine will not work. This, I think, is where reparative therapy suffers. The trope that's on offer is just too square. It's obviously the sort of thing that straight people would think up to explain homosexuality, but worse, it's the sort of thing that straight people would have thought up sixty years ago. It's in an outmoded, modernist, Freudian idiom that just seems weird and alienating to postmodern queerdom. It is, in short, tragically unhip.